modeling tillage effects on soil physical properties

Soil & Tillage Research, 20 (1991) 293-318 293 Elsevier Science Publishers B.V., Amsterdam

Modeling tillage effects on soil physical properties*

S.C. Gupta a, Birl Lowery b, J.F. Moncrief ~ and W.E. Larson a aDepartment of Soil Science University of Minnesota, St. Paul, MN 55108, USA bDepartment of Soil Science, University of Wisconsin, Madison, ~ 7 53706, USA

(Accepted 31 January 1991 )

ABSTRACT

Gupta, S.C., Lowery, B., Moncrief, J.F. and Larson. W.E., 1991. Modeling tillage effects on soil ph.vs- ical properties. Soil Tillage Res., 20:293-318.

Tillage refers to the manipulation of soil by an implement powered by humans, animals or machines. Tillage operation generally create two zones: ( 1 ) a zone where soil has been fractured and then turned over leading to rough surface conditions; and (2) a zone where soil has been compacted by the weight of the machinery. Thus, modeling tillage effects on soil physical properties involves t~o separate approaches depending upon the zone under consideration.

Modeling tillage systems offers an opportunity to: ( 1 ) synthesize the extensive experimental data in the literature: (2) develop tools for site specific management recommendations; and (3) identi~ areas of research where additional information is needed. Modeling tillage systems involves modeling the soil physical, chemical and biological properties and processes and then linking them with crop growth models to simulate crop yields or environmental impacts. This paper reviews models for predicting tillage effects on state soil physical properties. Specifically, we reviewed models which predict bulk density, surface microrelief, aerodynamic roughness length, water retention characteristics, h.v- draulic conductivity function, thermal conductivity, volumetric heat capacity and gas diffusion coefficient. Since most of the existing models for predicting soil physical properties are developed for untilled soils, the paper outlines procedures to adapt these models to fractured and compacted zones in tilled soils. The paper also identifies specific assumptions that need both laboratory and field testing.

INTRODUCTION

Tillage refers to the manipulations of soil by an implement powered by humans, animals or machines (Schafer and Johnson, 1982). During tillage, soil is fractured and then turned over leading to rough surface conditions. The roughness of the surface after tillage depends upon the depth of tillage, type of tillage tool, texture and pre-tillage soil physical conditions such as density and wetness. Tillage done with machinery also produces a zone of compaction which is a function of the machinery weight. In addition, a compacted

*Contribution from the Minnesota Agric. Exp. Stn., Scientific Journal Series, Paper No. 18 871.

0167-1987/91/$03.50 © 1991 - - Elsevier Science Publishers B.V.

294 S.C. GUPTA ET AL.

zone (plow pan) at the base of the manipulated soil may also form because of smearing by the tillage tool. Thus, modeling the tillage effects on soil physical properties involves two separate approaches, one dealing with modeling of the fractured or disturbed zone and the other dealing with modeling of the compacted zone.

Modeling of tilled soil is relatively new. Except for the work of van Duin (1956), most of the model development on predicting tillage effects on soil physical properties and processes has taken place in the 1970s and 1980s. To date there are few comprehensive reports dealing with the modeling of physical properties and processes in tilled soils. The first comprehensive review of the modeling activities on this subject was made during a 1980 American Society of Agronomy Symposium "Predicting Tillage Effects on Soil Physical Properties and Processes" (Unger et al., 1982 ). Even in this publication, most of the chapters reviewed experimental work on the effects of tillage on soil physical properties rather than provide models to predict these properti6s. Most of the models described in the publication dealt with soil physical processes and assumed that either the models for predicting tillage effects on soil physical properties already existed or the input of tilled soil physical properties were experimentally measured values.

Soil physical properties may be categorized as: ( 1 ) state soil physical properties, such as bulk density, roughness, thermal conductivity, water retention characteristics and soil strength; or (2) behavioral soil physical properties, such as soil temperature, soil water content and soil air content (Schafer and Johnson, 1982). Since 1982, a limited review of the modeling research related to tillage effects on soil physical properties has been given in the literature (Hadas et al., 1988). This is partly because limited research has been reported on this subject. Much of the research on the modeling of tillage effects on soil physical properties has been on the prediction of soil compaction after the passage of a tractor tire (Stihne, 1953; Perumpral et al., 1971; Gupta and Larson, 1982; van den Akker and van Wijk, 1987; Raper and Erbach, 1991 ). Even in this area, the prediction has been confined to load effects on volumetric strain or bulk density and not to other soil physical properties related to flow processes or soil strength.

Historically, tillage has been an empirical science (Larson and Osborne, 1982). Modeling tillage systems offers a powerful tool to: ( 1 ) generalize sys- tematically the existing information relating behavioral soil properties such as soil temperature, soil water content, soil aeration and soil strength, to crop growth and yield; (2) develop site specific recommendations for tillage management systems; and (3) identify areas of research where additional information is needed. Modeling behavioral soil physical properties or soil physical processes (water, heat and air fluxes) is much advanced compared with the modeling of state soil physical properties such as water retention characteristics, hydraulic conductivity-water content relationship, gas diffusion

MODELING TILLAGE EFFECTS 295

coefficient, thermal conductivity and diffusivity, and soil strength. Linden (1979) presented models to account for the effect of tillage on various soil physical processes.

State soil physical properties are essential inputs to the models of soil physical processes and crop growth. In most existing models of soil physical processes and crop growth, state soil physical properties correspond to those of untilled soil conditions. Tillage effects in these simulation models are generally accounted for by varying the bulk density of the soils. The usefulness of existing soil physical process and crop growth models can be greatly enhanced if physical models are available that describe the effects of tillage on state soil physical properties. This paper reviews some of the models designed to predict soil physical properties and shows how they have been or might be adapted to simulate tillage effects.

MODELING SOIL BULK DENSITY

Bulk density refers to the mass of dry soil per unit volume. The density of the soil in the tilled zone is much lower than the density in the compacted zones. Lower density in the tilled zone results from the fracture of soil by tillage implements which leads to the formation of clods or aggregates. Gupta and Larson (1982) used their packing model (Gupta and Larson, 1979a) to simulate the density of an aggregated soil. The packing model is based on the concept that during the packing process, certain aggregates (donor) will be randomly enclosed in the void spaces of packing assemblages formed by other aggregates of larger radii (acceptors). Using this principle, the void spaces of an acceptor unit can be completely filled by the donor aggregates, partially filled with donor aggregates and partially air filled, or completely air filled. Random selection of donor and acceptor aggregate fractions in the packing model leads to a series of random packing densities for a given aggregate size distribution.

Gupta and Larson ( 1982 ) used the packing model to show the differences in density for several aggregate size distributions of Webster clay loam soil (Typic Haplaquoll). Input to the packing model included the proportion of various size fractions of aggregates in the soil, bulk density of each aggregate fraction, and the bulk density of an aggregate within each fraction. In general, the predicted bulk densities were close to the measured values (Table 1 ). As expected, the greater the dominance of large fractions, the lower was the bulk density of the aggregated soil. Since the model was tested by artificially packing a small volume (4.5 l) of aggregates in the laboratory, the packing model needs further testing on other soil types but more importantly in the tilled zone under field conditions. The field testing should address the questions: ( 1 ) can tilled soils be represented by an aggregate size distribution? (2) is the

296 s.c. GUPTA ET AL.

TABLE 1

Packing ,densities and geometric mean diameter of various aggregate size distributions of dry Webster clay loam. The dominant aggregate fractions within a distribution are indicated by bold type (adapted from Gupta and Ewing. 1991 )

Diameter (mm) Pb Pa (Mgm -3) (Mgm -3)

Distribution number (Percent aggregate by weight)

1 2 3 4 5 6 7

50.8-25.4 0.93 1.90 40.20 5.01 5.04 5.07 5.25 4.92 5.42 25.4-12.7 0.97 1.87 30.00 9.35 4.80 4.94 4.96 17.60 4.84 12.7-5.66 0.95 1.87 11.30 43.80 5.36 5.37 5.52 6.66 23.20 5.66-3.36 0.96 1.89 3.31 10.70 5.27 4.49 4.76 4.49 7.61 3.36-2.00 0.97 1.86 2.53 6.58 21.70 4.80 5.12 4.88 5.90 2.00-1.00 0.99 1.87 3.90 7.60 19.30 9.81 6.44 5.41 7.65 1.00-0.50 1.09 1.90 3.57 6.40 13.90 26.80 6.97 6.75 8.78 0.50-0.25 1.09 2.06 2.68 5.62 12.90 20.10 10.10 9.95 9.90 0.25-0.106 1.15 2.02 1.52 2.79 8.79 12.40 31.30 29.40 7.39 0.106-0.053 1.12 2.05 0.57 1.38 1.70 4.09 8.77 5.91 10.30 0.053-0.053 1.01 1.97 0.40 0.77 1.37 2.14 10.80 3.99 9.61

Geometric mean diameter (mm) 9.06 3.03 1.08 0.68 0.52 0.81 1.81

Bulk density (Mg m - j ) Measured 1.09 1.15 1.27 1.39 1.46 1.50 1.44 Predicted 1.08 1.20 1.26 1.32 1.33 1.33 1.35

placement of aggregates after tillage random? and ( 3 ) what is the variation in the aggregate size distribution in various sections of the tilled zone?

As mentioned earlier, the models simulating bulk density of the untilled zone are much developed than the models for predicting the density of the tilled zone. Models for predicting the density of untilled soils have also been labeled as soil compaction models. Gupta and Allmaras (1987), Gupta et al. ( 1989 ) and Gupta and Raper ( 1991 ) reviewed some of the soil compaction models in the literature. Most of these models are based on the elastic stress- strain theory which states that the displacement in a body caused by an applied load is directly proportional to the load. Existing soil compaction models can be categorized into two broad groups: (1) analytical models; and (2) finite element models.

Analytical models

These models first calculate the distribution of stresses from an externally applied load and then convert these stresses into volumetric strains or bulk densities, based on the measured stress-strain relationship of a given soil. The calculation of stress distribution is based on the analytical solution of stress distribution in a homogeneous, isotropic, semi-infinite elastic medium


under a point load at the surface. The solution was first proposed by Boussi- nesq (1885) and later modified by Fr6hlich (1934).

S~Shne (1953) was the first to apply the modified Boussinesq equation to predict the stress distribution in the soil from an agricultural vehicle. The procedure involved dividing the contact area between tires and ground into 25 load elements in whose center of gravity a fraction of the surface load was applied as a concentrated load. The main stress at a point in the soil profile was then calculated from the summation of vertical, horizontal and tangential stresses from 25 load elements. S~Shne ( 1953 ) used the measured relationship between the applied stress and volumetric strain on a thin soil sample to convert predicted main stress into the soil displacement. Based on the concepts ofS~hne ( 1953 ), Gupta and Larson ( 1982 ) and van den Akker and van Wijk (1987) independently developed models to predict the distribution of applied stress after the passage of an agricultural vehicle. Predicted iso-stress lines in the model of Gupta and Larson (1982) were converted to iso-bulk density lines using the laboratory measured uniaxial stress-strain relationship (Gupta and Larson, 1982). This procedure assumes that the major prin- cipal stress in S~Shne's calculation and the vertical stress in a uniaxial test are equivalent. Gupta et al. (1985) tested this model on a Waukegan silt loam (Typic Hapludoll) and a Doland loam (Udic Haploboroll) in above-ground soil bins in Minnesota and in-situ on a Nahal Oz silt loam (Calcic Malic Hap-

J 150

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so <3

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298 s.c. GUPTA ET AL

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loxeralf) in Israel. The soil compaction model under-predicted the mechanical stress profile (Fig. 1 ) but the predicted bulk density profiles (Fig. 2 ) were close to the measured values. The maximum deviation between predicted and measured bulk densities were 0.12, 0.13 and 0.33 Mg m -3 for Waukegan silt loam, Doland loam and Nahal Oz loam, respectively.

Finite element model

The basis of a finite element model is the discretization of the soil contin- uum into assemblages of a finite number of elements that are connected at the nodal points (Fig. 3 ). The displacement at each nodal point caused by an externally applied stress is calculated using a displacement function that sat- isfies the compatibility conditions at all times. In most soil compaction models, the stress-strain relationship is taken to be similar to that of a linear elastic material (Gupta and Raper, 1991 ). Raper and Erbach (1990) successfully predicted the stresses beneath a fiat loaded circular steel plate using the finite element soil compaction model. Most of the predicted stresses were within the 95% confidence interval of the measured values. However, recent testing of the model (Raper et al., 1990) showed that stress prediction in the soil profile exceeded the 95% confidence interval.

MODELING SOIL SURFACE MICRORELIEF

Soil microrelief refers to the description of peaks and valleys created after the passage of a tillage tool. Several types of analysis have been suggested (Allmaras et al., 1967; R~mkens and Wang, 1986; Linden and Van Doren, 1986; Freebairn and Gupta, 1990) to summarize the microrelief data as one or two indices. All indices are a statistical measure of the randomness in the point heights taken over the tilled surface. One of the most common indices used in tillage research is the roughness index defined as the standard deviation of the pin heights (Z~) around the mean value (Z) after slope and tillage orientation in both directions has been removed:

RR__ N/Z n - 1 (1)

where RR is an index of random roughness and n is the number of pin heights. Allmaras et al. ( 1967 ) suggested that since the pin heights were log-normally distributed after slope and tillage orientation in both directions had been removed and the top and bottom ranked 10% of height data are excluded, they defined the random roughness as the standard deviation of the natural loga- rithms of corrected pin heights.

Zobeck and Onstad (1987) reviewed the literature for the effects of tillage

300

TABLE 2

Average random roughness values for and Onstad, 1987)

S.C. GUPTA ET AL.

several tillage sequences and operations (adapted from Zobeck

Single tillage operations Random Multiple Random roughness tillage roughness (cm) operations (cm)

Large offset disk 5.0 Moldboard plow (MP) 3.2 Lister 2.5 Chisel plow (CP) 2.3 Disk (D) 1.8 Field cultivator (FC) 1.5 Row cultivator 1.5 Rotary tillage 1.5 Harrow (H) 1.5 Anhydrous applicator 1.3 Rod weeder 1.0 Planter 1.0

MP-D 1.8 MP-D-H 1.7 MP-D-D-H 1.2 MP-FC 1.4 MP-FC-FC 1.3 No till 0.7 Smooth 0.6

and rainfall on random roughness. They presented an average random roughness value (RR o) for several tillage sequences and operations (Table 2). They further suggested the following regression equation to describe the degrada- tion of random roughness caused by rainfall (RRp):

RRp = O. 89RRo e - 0.026P ( 2 )

where P is the rainfall amount in centimeters. Random roughness calculations were based on the procedure of Allmaras et al. ( 1967 ).

Physically based models for predicting the microrelief or random roughness of soil after tillage by various tillage tools are rather limited. Gupta and Ewing ( 1991 ) suggested a procedure to simulate the microrelief and thus the random roughness of a soil based on the bulk density prediction from the packing model. The procedure involved simulating 100 random packing densities of a tilled (aggregated) soil using the packing model. Packing densities were then converted to pin heights using the weight of the soil in each cell and its corresponding cross-sectional area. Gupta and Ewing ( 1991 ) assumed that 100 predictions of the random densities corresponded to 100 equal size cells in an area 1 m by 1 m (A). The weight of the soil in each cell was assumed to equal 1/100 of the weight of the soil in an area 1 m by 1 m (Ws). The weight of the soil in the 1 m by 1 m area was calculated from the bulk density (Pb) of the untilled soil and the depth of tillage (D)


Ws=&AD (3)

W _ (4) t/

w - ( 5 )

p,a Z~

where: w is the weight of the soil in each cell; n is the number of cells in A, a is the area of each cell and Pi is the bulk density of each cell predicted from the packing model. In this study, Gupta and Ewing ( 1991 ) assumed that the bulk density of untilled soil was equal to the random packing density predicted from particle size distribution and the organic matter content of the soil (Gupta and Larson, 1979a).

Figure 4 shows an example of the simulated surface terrain of an aggregated Webster clay loam using the packing model. The surface terrain corresponded to the aggregate size distributions No. 1 (Fig. 4a), No. 3 (Fig. 4b) and No. 5 (Fig. 4c) in Table 1. As expected, Fig. 4 shows that the pin heights above the reference plane (surface before tillage) were higher for aggregate size distribution containing larger aggregates (distribution No. 1 ) than for those containing smaller aggregates (distributions No. 3 and No. 5 ).

Gupta and Ewing ( 1991 ) also showed that for a given aggregate size distribution, the greater the depth of tillage, the greater was the pin heights (Fig. 5 ). The authors reasoned that in addition to the differences in aggregate size distribution between different tillage systems, the depth of tillage was another important variable affecting the microrelief of the tilled surface. The greater variation in microrelief at higher depth of tillage was caused by the increased soil volume disturbed during tillage. Sensitivity analysis also showed that RR

TABLE 3

Predicted random roughness of seven aggregate size distributions as a function of three depths of tillage (adapted from Gupta and Ewing, 1991 )

Distribution GMD Depth of tillage (mm) 5 15

Random roughness (ram) 25

1 9.06 2.4 7.2 11.9 2 3.03 2.6 7.9 13.1 3 1.08 2.3 7.0 11.6 4 0.68 2.2 6.5 10.8 5 0.52 2.0 6.0 10.0 6 0.81 2.8 8.3 13.7 7 1.81 2.3 6.8 11.4

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(eqn. ( 1 ) ) was about the same for all seven aggregate size distributions but increased with an increase in depth of tillage (Table 3). This suggested that the greater roughness in moldboard plowed soil was largely caused by the greater depth of soil disturbance and not by the presence of large aggregates.

The model provides a framework that can be further extended to estimate the storage of water and snow in the depressional areas of the tilled surface. The model has not yet been tested. Specific assumptions that need testing are the same as outlined for the use of the packing model on tilled soils,

MODELING ROUGHNESS LENGTH

Roughness length or roughness parameter refers to the aerodynamic roughness of a given surface and is defined as the height below which the wind speed is zero (Rosenberg et al., 1983).

U(z) = - ~ l n z~ (6)

where U(z) is the mean wind speed at height z, k is von Karman's constant (with a value of about 0.4), and u. is the friction velocity and Zo is the roughness parameter. Several of the aerodynamic and combination methods of estimating evaporation include wind speed and in turn the roughness length in their calculations (Rosenberg et al., 1983). For example, van Bavel (1966) derived the following expression for calculating evaporation:

LE= _s( R. + S) + yLBv( e~ -ea) (7) s+?

where: LE is the latent heat flux; s is the slope of the saturation vapor pressure curve at the mean wet bulb temperature of the air, y is the psychrometric constant; R, is the flux density of net radiation; S is the soil heat flux; L is the latent heat of vaporization; and es and ea are the saturation and partial pressure of water vapor in air, respectively. Bv is defined as:

B,, _p~(k~ U(z) (8) P [ln (Z/Zo)l 2

where: p~ is the density of moist air; P is the atmospheric pressure; and E is the ratio of molecular weight of water to that of air.

Since tillage increases the area of the exposed soil surface, it is well known that the rate of evaporation from a tilled surface is greater. One additional parameter that influences this change in the rate of evaporation is the roughness length. To describe the process of evaporation from a tilled surface completely, models are needed that can convert the physical measurements of surface roughness (like pin heights) to an equivalent roughness length, z0.


Lettau (1969) presented a model to calculate the roughness length based on the effective obstacle height, h* (cm); the area seen by the wind in the approach towards the individual obstacle or the frontal area of the obstacle, as (cm)'-; and the plane area described by the local earth-air interface or the basal area per obstacle, As (cm)2.

Zo = O. 5 h ' a s ~ A s ( 9 )

where 0.5 is the average drag coefficient per obstacle. Van Doren and All- maras (1978) used Lettau's (1969) model to estimate the roughness length of the freshly plowed field, slaked soil surface, standing grain stubble and matted grain straw. The estimates were within the range of values often reported in the literature. The model needs additional field testing on surfaces that have been tilled by various tillage implements. Research is also needed to see if the roughness terrain (Figs. 4 and 5) simulated by the Gupta and Ewing ( 1991 ) model for aggregated soils can be used in Lettau's ( 1969 ) model to calculate the roughness parameter of the tilled surfaces.

MODELING SOIL WATER RETENTION CHARACTERISTICS

Soil water retention characteristics refer to the potential energy of soil water at various degrees of soil saturation (Hillel, 1980). Various attempts have been made to model the water retention characteristic of soil using the easily available soil parameters like particle size distribution and bulk density. These attempts include the regression (Gupta and Larson, 1979b; Rawls et al., 1982 ) and physico-empirical approaches (Arya and Paris, 1981 ). Regression models of water retention have been incorporated in several models (Shaffer and Larson, 1987; Williams et al., 1989) that simulate, among other processes, the water flow and crop growth. In these water flow and crop growth models, the tillage event is simulated by changing the bulk density of the surface layer. The effect of tillage on water retention characteristics is included by predicting the soil water retention characteristics at a new bulk density. The disad- vantage of these regression approaches to simulate tillage effects is that they treat the soil as a homogeneous system and do not consider the formation of two domains (pore space in the aggregate and pore space between the aggregates) caused by tillage.

Using the physico-empirical model of Arya and Paris (1981), Gupta and Ewing ( 1991 ) suggested a procedure that incorporates the effects of two domains resulting from tillage in the predicted water retention characteristic. Arya and Paris' model is based on the assumption that the shape of the particle size distribution and soil water characteristics curves are similar and it is essentially a matter of converting particle sizes into pore sizes and the corresponding volume of particle into pore volume. The steps in the Arya and Paris model involve dividing the particle size distribution curve into a num-


ber of discrete fractions and calculating equivalent pore volumes and corresponding pore radii from the mass of each discrete fraction and the bulk and particle densities of soil.

V,. = (w, /pp)e (10)

ri =Ri [4en~ l -P) /6 ]o.5 ( 1 1 )

2Y cos 0 g, = (12)

pgri

where: V, and w~ are the pore volume and weight of the ith fraction, respectively; pp is the particle density; e is the void ratio; r~ and R~ are the mean pore and particle radii of the ith fraction, respectively; n~ is the number of particles in the ith fraction; g4 is the soil matric potential; ? is the surface tension; 0 is the contact angle; p is the density of water; g is the acceleration due to gravity; and 11 is an empirical constant equal to 1.38. The formulation of pore radii is based on the assumption that the particles are spherical and pores are cylindrical.

Gupta and Ewing's ( 1991 ) adoption of the Arya and Paris model for tilled soil is based on the hypothesis that soil pore space can be divided into: ( 1 ) pore space in the aggregates (intra), and pore space between the aggregates (inter). Thus, the Arya and Paris model is used in two steps to predict: ( 1 ) the water retention characteristics of pores in the aggregates based on particle size distribution and density of an aggregate; and (2) the water retention characteristics of pores between the aggregates based on aggregate size distribution and bulk density of the soil. The two water retention characteristics are then summed in proportion to inter- and intra-aggregate pore space to predict the water retention characteristics of the aggregated or tilled soil. The proportion of inter-aggregate (Ie) and intra-aggregate (Ia) pore spaces are defined as follows:

I¢ = [(1 - -Pb/Pa)] I f (13)

I~ = 1--Ie (14)

f = ( 1 --Pb/Pp) ( 15 )

where: Pa is a weighted average density of an aggregate representing all aggregate fractions in a soil; Pb and pp are the bulk and particle densities of the soil, respectively; and f i s the total porosity.

Figure 6 shows an example of the predicted water retention characteristic curve of inter- and intra-aggregate pores and the combined pore space of an aggregated Webster clay loam (Gupta and Ewing, 1991 ). Curves in Fig. 6 represent aggregate size distribution No. I in Table I. As expected, Fig. 6 shows that for an aggregated soil, a large proportion of water at high matric


0.~ ¸ DISTRIBUTION #1

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Matric Potential, kPa

Fig. 6. Predicted inter-, intra-, and combined water retention characteristics of aggregated Webster clay loam (adapted from Gupta and Ewing, 1991 ).

0.5

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Matrie Potential, kPa

Fig. 7. Predicted water retention characteristics of three different aggregate size distributions of Webster clay loam (adapted from Gupta and Ewing, 1991 ).

potentials is retained in the pores between the aggregates, whereas a large proportion of water at low matric potentials is held in the pores of the aggregates. Gupta and Ewing ( 1991 ) also showed that the dominating pore size was directly related to the aggregate fractions that were dominating in a given aggregate size distribution (Fig. 7 ). For example, in aggregate size distribution No. I, the dominating fractions correspond to 50.4-25.4 and 25.4-12.7 mm diameter aggregates, whereas in aggregate size distributions No. 3 and No. 5, the dominating fractions corresponded to 3.36-2.00 and 2.0-1.0; and 0.250- 0.106 and 0.106-0.053 mm, respectively. Thus, a greater proportion of water is retained at high matric potentials (> - 3 kPa) for soils with large aggregates (distribution No. 1 ), at medium matric potential ( - 10 to - 2 0 0 kPa) for soils with medium size aggregates (distribution No. 3 ), and at low matric potentials ( < - 4 0 0 kPa) for soils with fine aggregates (distribution No. 5 ).

The procedures suggested by Gupta and Ewing ( 1991 ) to adopt the Arya and Paris ( 1981 ) model for the prediction of water retention characteristics


of aggregated soils have not been tested yet. Besides the assumptions outlined in the section on modeling of surface microrelief regarding representation of tilled soils by an aggregate size distribution, the question that should be an- swered before the Arya and Paris model can be successfully applied to tilled soil is: what is an appropriate value of fl for pores between the aggregates? Both Arya and Paris ( 1981 ) and Schuh et al. ( 1988 ) showed that fl deviates from 1.38 for large particles and thus, at high soil matric potentials. Gupta and Ewing ( 1991 ) assumed fl equalled 1.38 for both pores in and between the aggregates.

MODELING SOIL HYDRAULIC CONDUCTIVITY

The authors are unaware of any study in the literature dealing with the physical modeling of tillage effects on soil hydraulic conductivity-water content relationship. Tillage effects on hydraulic conductivity function have mostly been incorporated through the change in bulk density and not physically modeled as inter- and intra-aggregate pore space.

The existing models of soil hydraulic conductivity assume that pores in untilled soil can be represented as a bundle of capillaries whose radii are represented by the pore size distribution function or water retention characteristics curve (Childs and Collis-George, 1950; Marshall, 1958; Millington and Quirk, 1961 ). By calculating the mean neck radii at various degrees of saturation, the hydraulic conductivity function is calculated from the Poiseuille's law of flow through a capillary tube. A review of these methods was given by Brut- saert (1967), Green and Corey ( 1971 ) and Mualem (1986).

Mualem (1976) presented a simple analytical model to predict the hydraulic conductivity function from the water retention curve and the measured hydraulic conductivity at saturation. The model is similar to the model of Childs and Collis-George ( 1959 ) but uses a modified assumption concern- ing the hydraulic conductivity of pore sequence in order to take into account the large pore section

K,(O)=O°'s[ °, ] (16) .o) K,(O)=K(O)IK, at (17)

(18) where: K,(O) is the relative hydraulic conductivity; K(O) is the calculated hydraulic conductivity at a given effective degree of saturation (O); Ksat is


the measured saturated hydraulic conductivity; h is the soil matric head; and 0~t and 0r are the saturated and residual water contents, respectively; and 0 is a given water content. By using the following general equation (eqn. ( 19 ) ) to represent the water retention equation, van Genuchten (1980) presented a closed form equation (eqn. (20)) of the Mualem (1976) model to predict the hydraulic conductivity function for a given soil.

1 " O=(l q_(ah),, ) (19)

Kr(O)=005[l- ( 1 - O t /m)"]2

rn=l-1/n (20)

( 0 < m < l )

where: a, n and m are the parameters that describe the water retention characteristic curve. Van Genuchten (1980) presented a procedure to calculate the parameters of eqn. (19) from known water retention characteristic curves.

Existing models (Mualem, 1976; van Genuchten, 1980) for predicting hydraulic conductivity from soil water retention characteristics can be extended to tilled Soils provided the tillage effect on the pore size distribution or water retention characteristics can be simulated. We used van Genuchten's (1980) procedure on water retention characteristics in Fig. 7 to predict the hydraulic conductivity function of three aggregate size distributions described earlier. Figure 8 shows the relative hydraulic conductivity function for three aggregate size distributions as calculated using eqn. (20). In these calculations, we assumed that the residual water content was equal to 0.0, 0.03 and 0.04 for aggregate size distributions No. 1, No. 3 and No. 5, respectively. At any given relative water content, the relative hydraulic conductivity is higher for distribution dominated by large aggregates (distribution No. 1 ), followed by medium size (distribution No. 3) and then small size (distribution No. 5) aggregates. Since it is expected that the saturated hydraulic conductivity of the

I0 0

Io g

Io -*2 ~ j¢ .-.171.., D1ST #3 " / J- DIST #5

io -16"

0 .0 012 014 016 0,8 I,O O

Fig. 8. Predicted relative hydraulic conductivity, Kf (O), as a function of normalized water content, O, for aggregate size distributions No. 1, No. 3 and No. 5.


distribution dominated by large aggregates will be higher than the medium and small size aggregates, this will also result in higher hydraulic conductivity at a given water content for distribution No. 1 as compared with distributions No. 3 and No. 5.

All existing models of predicting hydraulic conductivity assume that Dar- cy's law applies to the soil conditions under consideration. In other words, the flow is laminar. If these models of predicting hydraulic conductivity are to be extended to tilled soils, then research is needed to test whether the assumption of laminar flow holds in large voids between the aggregates or not.

MODELING SOIL THERMAL PROPERTIES

Soil thermal properties refer to soil volumetric heat capacity, and soil thermal conductivity and diffusivity. Modeling thermal properties of tilled and untilled zones has been relatively straightforward and is generally based on the procedures suggested by de Vries ( 1963 ). The procedure assumes that the soil thermal properties are some weighted function of the thermal properties of its component. For example, the volumetric heat capacity (Cv) is defined as:

Cv....~.CmXm ~-CoXo ~-CwXw-~-CaXa ( 2 1 )

where: symbols C and X refer to the volumetric heat capacity and volume fraction, respectively; and subscripts m, o, w and a correspond to the mineral fraction, organic fraction, water content and air content, respectively. The volumetric heat capacity of mineral fraction, organic matter, water and air is 2.00, 2.51, 4.19 and 0.12 MJ m -3 K - l , respectively (de Vries, 1963). The effect of tillage and compaction on volumetric heat capacity can be simulated by accounting for the change in the relative proportion of water and air as a result of tillage or compaction.

The model for calculating soil thermal conductivity is based on the theory for predicting the dielectric constant of a granular material (de Vries, 1963 ). The theory assumes that the soil thermal conductivity (2) is some weighted function of the thermal conductivity of its component (/q.~) and the weight (k~) is defined as the ratio of the average temperature gradient across the particles of a given component to the average gradient of the medium as a whole.

N N

2 = ~_, k iX i2 i / ~., ](iX i ( 2 2 ) i= 1 i= I

where N is the number of distinct components. The value of ki can be calculated from:

MODELING TILLAGE EFFECTS 31 1

1 1 2 ki=-~[l+(-~o-l)gi 1- + ~ I 1 + ( 2 ~ - ~ - 1 ) ( l - 2 g i ) ] - (23)

where: 20 is the thermal conductivity of continuous phase; and gi is shape factor of the particles of the ith component. In the above equation, de Vries (1963) assumed that the particles of soil and its component are ellipsoidal and thus the shape factor in the x and y direction are equal. De Vries ( 1963 ) gave g, values of 0.144, 0.125 and 0.5 for quartz, clay minerals and organic matter, respectively, and assumed that the shape factor for water and air de- pended upon the degree of saturation.

De Vries (1963) further assumed that when water is a continuous phase and the humidity of the soil air is near 100%, the conductivity of air in the soil was a sum of the conductivity of dry air plus the contribution to conductivity caused by vapor distillation. When the humidity of the soil air was less than 100%, the conductivity of the soil air corresponded to that of the dry air. The maximum value of the shape factor for air (ga) was assumed to equal 0.33. This implied that globules near saturation were spherical in nature. The thermal conductivity of soil components corresponded to 8.79, 2.93, 0.25, 0.57 and 0.03 W m -1 K -~ for quartz, clay minerals, organic matter, water and air, respectively. Kimball et al. (1976) tested the de Vries' values ofga for Avondale loam. These authors concluded that ga values from de Vries' theory were too high and the best predictions of the heat fluxes for their soil was with the ga5 curve shown in Fig. 9.

De Vries' theory can be extended to tilled soils by assuming that two domains exist: ( 1 ) inter-aggregate pore space; and (2) intra-aggregate pore space. The procedure will involve, first calculating the thermal conductivity of an

J

0,5 t S 1.0

...........

° " . ; - o, ~ oo Wp S A T

O, cm 3 c m - 3

Fig. 9. Air shape factor curves, ga, and relative humidity, h, for Avondale loam versus volumetric water content, 0. The ga0 curve represents de Vries' (1963) theor).' whereas the ga5 curve is the best fit obtained by Kimball et al. (1976) in a field experiment (adapted from Kimball et al., 1976).


aggregate from the soil particle size analysis and bulk density of an aggregate and then calculating the thermal conductivity of the tilled soil from the thermal conductivity of aggregate and bulk density of the soil. However, one would need to evaluate the air-shape factor at various degree of saturation for the pore space between the aggregates. To the authors' knowledge, no report ex- ists in the literature on the nature ofga values as a function of soil wetness for tilled soils. Another important consideration that will need evaluation relates to the contribution of vapor distillation on soil thermal conductivity caused by the large voids in tilled soils. The question will be: is the vapor distillation greater because of turbulence (Hadas, 1977) than the amount accounted for by the theory?

MODELING GAS DIFFUSION COEFFICIENT

Molecular diffusion has been assumed to be the main mechanism control- ling the exchange of gases between the soil and the outside atmosphere on a daily basis. Besides the concentration or partial pressure gradient, the diffusion flux depends on the molecular diffusion coefficient which is controlled by the continuity and tortuosity of the soil pore system. Several types of relationships describing the diffusion coefficient to soil air-filled porosity have been given in the literature (Hillel, 1980). One of the most common forms of the relationships is:

Os/Oo =~fa (24)

where: Ds, Do are the gas diffusion coefficients in soil and air, respectively; is a constant of proportionality also defined as the tortuosity coefficient; and fa is the air-filled pore space. Penman (1940) found a value of 0.66 for thereby suggesting that the average apparent path is about two thirds of the length of the real path of diffusion in soil (Hillel, 1980). Since, both tillage and compaction alter the soil tortuosity, it is expected that the diffusion coefficient will be affected by both tillage and compaction. Currie (1983) proposed that the diffusion coefficient relationship to air-filled porosity in a uni- modal pore size distribution follows an exponential relationship of the form:

DffOo ~ f4 (25)

For a bi-modal pore size distribution such as tilled soil, Currie ( 1983 ) proposed that the gas diffusion coefficient follows an exponential function for the inter-aggregate pores and a linear relationship for intra-aggregate pores (Fig. 10). Since the effect of compaction is to narrow the pore size distribution, Currie (1984) suggested that the exponential form of the diffusion relationship shifts towards a linear form as soil compaction increases (Fig. 11 ).

Physical modeling of the gas diffusion coefficient based on the state soil properties such as texture, density and aggregate size distribution has been

MODELING TILLAGE EFFECTS

0.3

0.2

-- 0.1

0 0

Intercrumb =;4- Crumb--~l [ t I I

I I L

D~O O~ fa 4

4

t ~ t I I 0.1 0,2 0 .3 0 ,4 0.5 0.6

fa (cm 3 cm "3)

313

Fig. 10. Generalized relationship of D,/Do versus air content (.f~) of packed soil crumbs (adapted from Currie, 1983).

0.3

~ 0 . 2

0.1

0 0

f O

s (Mg ni 3 )

0 0 .86 1 0 .99 2 1 .06 3 1.12 4 1 .20 5 1 .29

I l I

0.1 0.2 0.3 0.4 0.5 0.6 0.7

AIR CONTENT, fa (cm 3 cm "3)

Fig. 11. Relationship of DJDo versus air content of 1-2 mm soil aggregates at five levels of compaction (adapted from Currie, 1984).

rather limited. De Vries (1952) suggested that the apparent or mean diffusion coefficient in soil can be calculated using the weighted mean approach (eqn. (22)) suggested by the author for calculating the thermal conductivity of the soil (van Duin, 1956). Since the diffusion coefficient of soil solids and soil water is zero, eqn. (22) results in:

kaXaDo (26) Ds-k~Xs+k~Xw+kaX~

where: X and k are volume fraction and weighing constants, respectively; and subscript s, w and a correspond to solid, water and air, respectively. If air is a

314 s.c. GUPTA ET .-kL.

continuous medium, then by analogy with thermal conductivity, the weight- ing constants may be calculated as follows:

3a,b,cL \Do 1 ga (27)

When air is a continuous medium, ka is 1. Then, for solids and water eqn. (27) reduces to:

k l _ f 1 "~ ks~ w ~-- ~ a,~b~c ~k 1 - ~ a ~ (28)

If water and soil solids are considered as a dispersed phase, then eqn. (26) reduces to:

Ds X~ X$ (29) Do -X~ +k~(X$ +Xw) -X~ +ks( 1 -X~)

D $

D o

1.0

0.8

0.6

0.4

0.2

PENMAN'S RESULTS FOR SOILS PENMAN'S RESULTS FOR GLASS SPHERES

o PENMAN'S RESULTS FOR MICA SPHERICAL PARTICLES CYLINDRICAL PARTICLES AND DISC WITH n=3

- - - - - CYLINDRICAL PARTICLES WITH BLOCKED PORES - - ' - - DISC WITH n=10

DISC WITH n=100

J

, / /

/ o i

o l

/ / /

J _ . . . . . , . - -

/ J

0 0.2 0.4 0.6 0.8 1.0

A i r - F i l l e d P o r o s i t y , fa

Fig. 12. A comparison of predicted and measured relationship of Ds/Do versus volume of air- filled pores in a granular material (adapted from de Vries, 1950) (f~ is the same as X~ in eqn. (26)) ,


De Vries (1950) also introduced a reduction factor (r) when a portion of pores are blocked and the air-filled pores are not continuous.

1 - X o r= (30)

l+0.5Xo

where X0 is the volume fraction of blocked pores and is defined as:

Xo= (1--Xa)Xa (31)

where e is the total porosity. De Vries (1950) presented Ds/Do as a function of air-filled pore space for various shaped particles (Fig. 12 ) using the above procedure. As expected, D,/Do increases with an increase in air-filled pore space and the shape of the curves depends upon the shape of the granular material. De Vries ( 1950 ) obtained a good agreement between his theory and Penman's measurements of e as 0.4.

The procedure of de Vries (1952) and van Duin (1956) can be extended to tilled soil using the procedure described under the modeling of soil thermal conductivity i.e. soil pore space consists of two domains: ( I ) pores in the soil aggregates; and (2) pores between the aggregates. Now for each domain, the de Vries theory can be applied to estimate the gas diffusion coefficient. How- ever, further research is needed to define the limits of water content when air is continuous and water and solids are dispersed phase or vice versa, for pore space both in and between the aggregates.

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modeling tillage effects on soil physical properties

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